Answered: Step 1 The average cost function is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Step 1

The average cost function is given as A(q) = 125/q+ q²/16 -4, where q is the firm's output.

1. What part of the decreasing range is practically feasible?

2. Write an equation for the total cost function.

3. Hence calculate the level of output for which total costs are minimum.

Expert Solution

Step 1

Step 2

$\begin{array}{l} (1) \\ Consider the average cost function is \\ A (q) = \frac{125}{q} + \frac{q^{2}}{16} - 4, \\ where q is the firm' s output . \\ Now, differentiate the function A w . r . t q, then \\ A' (q) = - \frac{125}{q^{2}} + \frac{2 q}{16} \\ Put A' (q) = 0 \\ - \frac{125}{q^{2}} + \frac{2 q}{16} = 0 \\ - \frac{125}{q^{2}} + \frac{q}{8} = 0 \\ \frac{q^{3} - 1000}{8 q^{2}} = 0 \\ \Rightarrow q = 10 \\ \begin{matrix} No - & Domain & Behaviour of A' (q) & Nature \\ 1 & For q > 10 & A' (q) > 0 & Increasing \\ 2 & for q < 10 & A' (q) < 0 & Decreasing \end{matrix} \\ It shows that cost function is decreaing in the range of output q \in (0, 10) . \end{array}$

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